Permanent Color Thermocromatic Filament Idea

I've seen a lot of cool gifs about thermochromatic filament and I was wondering if there exists a filament which permanently changes color based on the temperature it was printed at. This would make it very easy to print ****multi-color prints without having a dual extruder, and it would also allow for a range of colors. Obviously there are many potential problems with the idea, but just a thought.